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Splines for financial volatility

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  • Francesco Audrino
  • Peter Bühlmann

Abstract

Summary. We propose a flexible generalized auto‐regressive conditional heteroscedasticity type of model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B‐splines of lagged observations and volatilities. Estimation of such a B‐spline basis expansion is constructed within the likelihood framework for non‐Gaussian observations. As the dimension of the B‐spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, and also in comparison with other approaches, and we present some supporting asymptotic arguments.

Suggested Citation

  • Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670, June.
    • Handle: RePEc:bla:jorssb:v:71:y:2009:i:3:p:655-670
    DOI: 10.1111/j.1467-9868.2009.00696.x
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    Cited by:

    1. Meister, Alexander & Kreiß, Jens-Peter, 2016. "Statistical inference for nonparametric GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 126(10), pages 3009-3040.
    2. Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, March.
    3. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    4. Wilson Ye Chen & Richard H. Gerlach, 2017. "Semiparametric GARCH via Bayesian model averaging," Papers 1708.07587, arXiv.org.
    5. Mittnik, Stefan & Robinzonov, Nikolay & Spindler, Martin, 2015. "Stock market volatility: Identifying major drivers and the nature of their impact," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 1-14.
    6. Yujiao Yang & Yuhang Xu & Qiongxia Song, 2012. "Spline confidence bands for variance functions in nonparametric time series regressive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 699-714.
    7. Hiroyuki Kawakatsu, 2022. "Local projection variance impulse response," Empirical Economics, Springer, vol. 62(3), pages 1219-1244, March.
    8. Souhaib Ben Taieb & Rob J Hyndman, 2014. "Boosting multi-step autoregressive forecasts," Monash Econometrics and Business Statistics Working Papers 13/14, Monash University, Department of Econometrics and Business Statistics.
    9. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," LIDAM Discussion Papers CORE 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Barrow, Devon K. & Crone, Sven F., 2016. "A comparison of AdaBoost algorithms for time series forecast combination," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1103-1119.
    11. Hugh Christensen & Simon Godsill & Richard E Turner, 2020. "Hidden Markov Models Applied To Intraday Momentum Trading With Side Information," Papers 2006.08307, arXiv.org.
    12. Nikolay Robinzonov & Gerhard Tutz & Torsten Hothorn, 2012. "Boosting techniques for nonlinear time series models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 96(1), pages 99-122, January.
    13. Audrino, Francesco & Meier, Pirmin, 2012. "Empirical pricing kernel estimation using a functional gradient descent algorithm based on splines," Economics Working Paper Series 1210, University of St. Gallen, School of Economics and Political Science.
    14. Ozer Ozdemir & Memmedaga Memmedli & Akhlitdin Nizamitdinov, 2013. "ANN Models and Bayesian Spline Models for Analysis of Exchange Rates and Gold Price," International Econometric Review (IER), Econometric Research Association, vol. 5(2), pages 53-69, September.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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